Passive nonreciprocal amplifier coupling network



21, 1954 B. D. H. TELLEGEN ETAL 7,759

PASSIVE NON-RECIPROCAL AMPLIFIER COUPLING NETWORK Filed Feb. 26, 1952 Z. i 5 [IN/I "m: /o--l- 1 INVENTORS Bernurdus Dominicus Huberrus Tellegen Wil em N'jenhuls By W United States Patent PASSIVE NONRECIPROCAL AMPLIFIER COUPLING NETWORK Bernardus Dominicus Hubertus Tellegen and Willem Nijenhuis, Eindhoven, Netherlands, assignors to Hartford National Bank and Trust Company, Hartford,

Conn.,astrustee I Application February 26, 1952, Serial No. 273,514 Claims priority, application Netherlands March 1, 1951 Claims. (Cl. 179-171) timum transmission impedance Z21 obtainable with thisprescribed frequency dependence at given values of the input capacity C1 and the output capacity C2 of the quadripole.

The invention is characterized by the use of a nonreciprocal electric quaripole, in which the quadripole impedances Z11, Z12, Z21 and Z22 fulfill the following conditions for all applied frequencies:

where R and X designate the real and the imaginary part of the associated impedance Z respectively; p=jw; w=the angular frequency; P designates a never negative rational function in 11 C1 and C2 are the input capacity and the output capacity respectively of the quadripole; b1, b2 are positive real constants or pairs of conjugate complex constants having a positive, real part; '(P)= (-P)- The invention is based on the following considerations: The following relation prevails between the voltages V and the currents I at the input terminals 1 and the output terminals 2 respectively of a quadripole 3 (Fig 1), having an input capacity C1 and an output capacity C2:

where Z11 and Z22 designate the input impedance and the output impedance respectively; Z21 is the transmission impedance and Z12 is the reaction impedance of the quadripole. The conventional, reciprocal quadripole fulfills the reciprocity relation: Z12=Z21.

A predetermined frequency variation of Z21 is, in general, prescribed for a quadripole connected between the output electrode of a first amplifying tube 5 and the input electrode of a second amplifying tube 6 (Fig. 2). It is desired that the optimum value for this transmission impedance Z21 be found using the given values of the capacities C1 and C2 which are produced by the wiring and the parasitic tube capacities. In other words, the transmission impedance Z21 is prescribed apart from a multiplicative constant. At the given input capacity C1 and output capacity C2 these constants are made as large as possible.

Bode solves this problem for a reciprocal quadripole (see Bode: Networks Analysis and Feedback Amplifier Design, chapter XVII) by assuming that the transmission impedance Z21 is completely given; he then determines theconditions in which the input capacity C1 a'nd1the 2,697,759 Patented Dec. 21, 1954 output capacity C2 become maximum in the given ratio' C1/C2. Subsequently the values of the impedances found can be multiplied by the same factor, so that the values of the input capacity and the output capacity become equal to the given values of C1 and C2 respectively. The transmission impedance Z21 is multiplied by the same factor, so that then the maximum value of this transmission impedance Z21 is found.

According to Bode the conditions for a realisable quadripole are:

R11(w)R22(w) R 21(w) where R(w) indicates the real parts of the associated impedances Z(jw) where w designates the angular frequency and the conditions for maximum input capacity and output capacity are that with given C1/C2 2 w= o 2 2C, are minimum.

In order to fulfill these conditions, it is necessary, according to Bode, that for each value of the frequency.

As is shown in Fig. 3, the real part R21 of thetransmission impedance Z21 will, as a rule, not be mvariably positive or negative, but it will have alternate polarities.

and

' However, since the virtual parts R11 and R21 of the input impedance and the output impedance respectively must be proportional to the absolute value of R21, 3 kink, at the frequencies m1, m2 and an, will occur in the frequency characteristic for these impedances. This proves that the associated network must, in theory, be of infinitely high order, even if Z21 is of finite order.

In the circuitarrangement according to the invention, use is made of a non-reciprocal, electric quadripole. Such non-reciprocal, electric quadripoles are described,

. for example, in the U. S. patent applications Serial No.

13,506, now Patent No. 2,647,239, issued July 28, 1953, and Serial No. 241,835, filed August 14, 1951. They have the property that the impedances Z21 and Z12 are not equal. As a condition for a realisable quadripole is and the conditions for a maximum input capacity and output capacity are again that at given. values of C1/ C2:

that it becomes possible to form the complete square of a never negative, rational function P in w, where and 1 in which case the network becomes of finite order, since the impedanees R11 and R22 must be describable, as

tion is found:

I: ,6Z2)d s a J;Re 1 w (l where Z"(p)==Z(p) at p=iw, and Re designates the real part of the next following complex functions. The

condition 61 is zero is fulfilled, according to one of the integral theses of Bode, if the integrant can represent the real part of a passive impedance function, of which the denominator exceeds the numerator by at least two degrees. This is the case, if

can be written, where b1, b2 designate positive real constants or pairs of conjugate complex constants having a positive real part.

It is found that a network in which the impedances Z21 and Z12 fulfill the condition (10) and which, consequently, has the optimum transmission impedance Z21, fulfills at the same time the condition so that it remains of finite order, it being assumed that Z21 remains of finite order.

The condition (4) is furthermore fulfilled, as can be proved, by each non-reciprocal quadripole, in which all losses are concentrated in only one resistor.

An example has been described of a non-reciprocal quadripole, connected between the anode circuit of a first amplifying tube and the grid circuit of a second amplifying tube, in which tuned oscillatory circuits are connected in parallel with the input terminals and the output terminals and in which furthermore a resistance coupling is provided between the primary terminals and the secondary terminals of the quadripole, so that a bandpass filter is obtained having an appreciably higher transmission impedance than is obtainable with a non-reciprocal quadripole. The invention has for its object to provide quadripoles which lead to another transmission function than is obtainable with the use of a bandpass filter comprising only two coupled circuits; it therefore explicitly excludes a claim for the aforesaid case.

A few examples of networks are described hereinafter, which fulfill the conditions (5), (6) and (10) in accordance with the invention.

I. It is assumed that the desired transmission impedance is represented by 1 p2+ p+b2 The modulus of this transmission function is indicated in Fig. 4 for a high value of b/c. The impedance Z12 must then, be represented by Thisis the case, if

a2b K For the quadripole impedani es is thus found:

z,,=;j ;%-zm

Z2 a+2p 5 This network may be obtained, as is shown in Fig. 5, by assuming that the capacities C1 and C2 are identical. The values in this case are:

Capacities C=b+ /za gyration conductance s: b b /2 a) resistor R= /2a(b+ /2a) Compared with a reciprocal network, in which b2 l p2 now a network of finite order is found, of which the transmission impedance is a few times higher.

II. It is assumed that the desired transmission impedance is represented by:

where b is a real positive constant and Y is an admittance, equal to the quotient f/g of two polynomials, of which the numerator is of the same degree as the denominator or is one degree lower than the denominator. The corresponding network is shown in Fig. 6 and Fig. 7 respectively. Referring to Fig. 6, a gyration coupling is connected in parallel with the input terminals and the output terminals, having input capacity C1 and output capacity C2, which are again assumed to be identical and the admittance Y between one of the primary terminals and one of the secondary terminals is connected. In order to fulfill the condition (10) the impedance Z12 is found to be necessarily equal to UH-P) which is the case, if the factor Y+Y' is distributed. In the dlagrams shown in Figs. 6 and 7 the capacities C are 1, the gyration conductivity s=b and according to Fig. 7, the impedance Z is III. It is assumed that the desired transmission impedance can be represented by:

Z12: (f 9)H f U +g the condition (10.) is found to be fulfilled, since after division of the factor (fg and gf) the relation changes, in accordance with this condition, into:

The above relation for Z21 may, if desired, be changed into:

In the corresponding diagram of Fig. 8, for example, the transmission impedance may be described in the relation given, if the impedances X are equal reactances, which are substantially free from losses and if Y is an arbitrary admittance in which substantially all damping of the quadripole is concentrated.

What we claim is:

1. A circuit arrangement comprising first and second amplifier stages, each stage including an electron discharge tube having a control electrode and an output electrode, and a passive non-reciprocal quadripole coupled between the output electrode of the first stage and the input electrode of the second stage, said quadripole possessing electrical characteristics in which the following quadripole relations subsist for all applied frequencies:

where 2. A circuit arrangement as set forth in claim 1 wherein b1 and 112 are positive real constants.

where f and g=arbitrary polynomials H =a polynomial having only even powers of p E and U =the polynomials formed by the even and odd powered terms respectively of (l21+p) (b2-|-p) References Cited in the file of this patent UNITED STATES PATENTS Number Na Tellegen Date 2,647,239 July 28, 1953 OTHER REFERENCES Bode, Network Analysis and Feedback Amplifier Design, pp. 427-444, published by D. Van Nostrand CO., Inc., New York, 1945. (Copy in Scientific Library.)

Tellegen, Philips Research Reports, vol. 3, N0. 2, April, 1948, PP. 81-101. 

